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E Somfai

Publications and source records attributed to E Somfai.

6 recordsLinked to original sources
PubMed2003

Diffusion-controlled growth: theory and closure approximations.

We expand upon a new theoretical framework for diffusion-limited aggregation and associated dielectric breakdown models in two dimensions [R. C. Ball and E. Somfai, Phys. Rev. Lett. 89, 135503 (2002)]. Key steps are understanding how these models interrelate when the ultraviolet cut-off strategy is changed, the analogy with turbulence, and the use of logarithmic field variables. Within the simplest, Gaussian, truncation of mode-mode coupling, all properties can be calculated. The agreement with prior knowledge from simulations is encouraging, and a new superuniversality of the tip scaling exponent is discussed. We find angular resonances relatable to the cone angle theory, and we are led to predict a new screening transition in the DBM at large eta.

Journal Article↗
PubMed2002

Theory of diffusion controlled growth.

We present a new theoretical framework for diffusion limited aggregation and associated dielectric breakdown models in two dimensions. Key steps are understanding how these models interrelate when the ultraviolet cutoff strategy is changed, the analogy with turbulence and the use of logarithmic field variables. Within the simplest, Gaussian, truncation of mode-mode coupling, all properties can be calculated. The agreement with prior knowledge from simulations is encouraging, and a new superuniversality of the tip scaling exponent is both predicted and confirmed.

Journal Article↗
PubMed2001

Fluctuation effects in an epidemic model.

We study a discrete epidemic model A+B-->2A in one and two dimensions (1D and 2D). In 1D for low concentration theta, we find that a depletion zone exists ahead of the front and the average velocity of the front approaches v=theta/2. In the 1D high concentration limit, we find that the velocity approaches v=1-e(-theta/2). In 2D, for low concentration we also find a depletion zone, and the velocity scales as v approximately theta(0.6), which is different from the scaling expected from the mean field approximation, v approximately theta(0.5). Analysis of the interface width scaling properties demonstrated that the front dynamics of this reaction are not governed by the Kardar-Parisi-Zhang equation.

Journal Article↗
PubMed2001

Nothing moves a surface: vacancy mediated surface diffusion.

We report scanning tunneling microscopy observations, which imply that all atoms in a Cu(001) surface move frequently, even at room temperature. Using a low density of embedded indium "tracer" atoms, we visualize the diffusive motion of surface atoms. Surprisingly, the indium atoms seem to make concerted, long jumps. Responsible for this motion is an ultralow density of surface vacancies, diffusing rapidly within the surface. This interpretation is supported by a detailed analysis of the displacement distribution of the indium atoms, which reveals a shape characteristic for the vacancy mediated diffusion mechanism that we propose.

Journal Article↗